Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
8001	2^338224+185461	101816	Stefano Morozzi	03/2022
8002	2^338224+62295	101816	Stefano Morozzi	04/2022
8003	2^338225+162645	101816	Stefano Morozzi	04/2022
8004	2^338223+144209	101816	Stefano Morozzi	09/2022
8011	6^130841+103	101815	Lelio R Paula	10/2016
8005	2^338220+150405	101815	Stefano Morozzi	11/2021
8006	2^338219-4147	101815	Stefano Morozzi	01/2022
8007	2^338221+83391	101815	Stefano Morozzi	02/2022
8008	2^338221+62937	101815	Stefano Morozzi	04/2022
8009	2^338220-65697	101815	Stefano Morozzi	01/2023
8010	2^338220-139505	101815	Stefano Morozzi	01/2023
8012	2^338216+77473	101814	Stefano Morozzi	12/2021
8013	2^338218+155299	101814	Stefano Morozzi	01/2022
8014	2^338217-134745	101814	Stefano Morozzi	04/2022
8015	2^338218+73507	101814	Stefano Morozzi	11/2022
8016	2^338213-125631	101813	Stefano Morozzi	12/2021
8017	2^338215+25845	101813	Stefano Morozzi	12/2021
8018	2^338210-153537	101812	Stefano Morozzi	01/2022
8019	2^338209+60915	101812	Stefano Morozzi	03/2022
8020	2^338211-57297	101812	Stefano Morozzi	03/2022
8021	2^338211-110257	101812	Stefano Morozzi	06/2022
8022	2^338211+71549	101812	Stefano Morozzi	11/2022
8023	2^338208-178787	101811	Stefano Morozzi	01/2022
8024	2^338208+106153	101811	Stefano Morozzi	01/2022
8025	2^338207+16499	101811	Stefano Morozzi	06/2022
8026	2^338205+102471	101810	Stefano Morozzi	12/2021
8027	2^338199-176377	101809	Stefano Morozzi	12/2021
8028	2^338201-151233	101809	Stefano Morozzi	12/2021
8029	2^338202-152061	101809	Stefano Morozzi	12/2021
8030	2^338202+133785	101809	Stefano Morozzi	03/2022
8031	2^338200+135643	101809	Stefano Morozzi	03/2022
8032	2^338202+14169	101809	Stefano Morozzi	05/2022
8033	2^338202-85211	101809	Stefano Morozzi	06/2022
8034	2^338200+74265	101809	Stefano Morozzi	02/2023
8035	2^338196+121147	101808	Stefano Morozzi	11/2022
8036	2^338196+73551	101808	Stefano Morozzi	11/2022
8037	2^338194-175845	101807	Stefano Morozzi	12/2021
8038	2^338195+56771	101807	Stefano Morozzi	02/2022
8039	2^338195+162365	101807	Stefano Morozzi	04/2022
8040	2^338194+67497	101807	Stefano Morozzi	09/2022
8041	2^338193-116335	101807	Stefano Morozzi	01/2023
8042	2^338194-15585	101807	Stefano Morozzi	01/2023
8043	2^338192+130387	101806	Stefano Morozzi	01/2022
8044	2^338190+89359	101806	Stefano Morozzi	05/2022
8045	2^338189+144605	101806	Stefano Morozzi	09/2022
8046	2^338190-113537	101806	Stefano Morozzi	12/2022
8047	2^338186+127245	101805	Stefano Morozzi	12/2021
8048	2^338186-130013	101805	Stefano Morozzi	02/2022
8049	2^338186+39235	101805	Stefano Morozzi	05/2022
8050	2^338185+77315	101804	Stefano Morozzi	12/2021
8051	2^338185+102519	101804	Stefano Morozzi	12/2021
8052	2^338183-76539	101804	Stefano Morozzi	12/2021
8053	2^338185+104489	101804	Stefano Morozzi	01/2022
8054	2^338179+35361	101803	Stefano Morozzi	03/2022
8055	2^338181+64235	101803	Stefano Morozzi	05/2022
8056	2^338181+94047	101803	Stefano Morozzi	09/2022
8057	2^338180+146131	101803	Stefano Morozzi	11/2022
8058	2^338179+123399	101803	Stefano Morozzi	11/2022
8059	2^338182-42425	101803	Stefano Morozzi	02/2023
8060	2^338177+51807	101802	Stefano Morozzi	12/2021
8061	2^338177+107385	101802	Stefano Morozzi	02/2022
8062	2^338178+34287	101802	Stefano Morozzi	03/2022
8063	2^338178+184207	101802	Stefano Morozzi	03/2022
8064	2^338177-108901	101802	Stefano Morozzi	04/2022
8065	2^338177+141569	101802	Stefano Morozzi	06/2022
8066	2^338176+46221	101802	Stefano Morozzi	11/2022
8067	2^338175+25161	101801	Stefano Morozzi	11/2021
8068	2^338173-27901	101801	Stefano Morozzi	01/2022
8069	2^338174+23217	101801	Stefano Morozzi	11/2022
8070	2^338174+23793	101801	Stefano Morozzi	11/2022
8071	2^338173-36183	101801	Stefano Morozzi	12/2022
8072	2^338173-137053	101801	Stefano Morozzi	12/2022
8073	2^338174-36797	101801	Stefano Morozzi	12/2022
8074	2^338175-166509	101801	Stefano Morozzi	01/2023
8075	2^338169-155965	101800	Stefano Morozzi	02/2022
8076	2^338172+95797	101800	Stefano Morozzi	11/2022
8077	2^338171-117987	101800	Stefano Morozzi	02/2023
8078	2^338166+183237	101799	Stefano Morozzi	02/2022
8079	2^338168-157835	101799	Stefano Morozzi	03/2022
8080	2^338166+137107	101799	Stefano Morozzi	04/2022
8081	2^338166+22897	101799	Stefano Morozzi	11/2022
8082	2^338166-161123	101799	Stefano Morozzi	12/2022
8083	2^338165-152139	101798	Stefano Morozzi	12/2021
8084	2^338163-178947	101798	Stefano Morozzi	02/2022
8085	2^338164-64329	101798	Stefano Morozzi	01/2023
8086	2^338159-127575	101797	Stefano Morozzi	12/2021
8087	2^338161+154259	101797	Stefano Morozzi	01/2022
8088	2^338160+139947	101797	Stefano Morozzi	05/2022
8089	2^338160+191815	101797	Stefano Morozzi	09/2022
8090	2^338160+22207	101797	Stefano Morozzi	11/2022
8091	2^338161+196157	101797	Stefano Morozzi	11/2022
8092	2^338162-138635	101797	Stefano Morozzi	12/2022
8093	2^338156-75269	101796	Stefano Morozzi	12/2021
8094	2^338156-151247	101796	Stefano Morozzi	12/2021
8095	2^338156+103273	101796	Stefano Morozzi	01/2022
8096	2^338156+167053	101796	Stefano Morozzi	09/2022
8097	2^338158+69303	101796	Stefano Morozzi	09/2022
8098	2^338158+171189	101796	Stefano Morozzi	11/2022
8099	2^338157-188989	101796	Stefano Morozzi	12/2022
8100	2^338158-188711	101796	Stefano Morozzi	12/2022
8101	2^338155+132621	101795	Stefano Morozzi	02/2022
8102	2^338155-82605	101795	Stefano Morozzi	03/2022
8103	2^338155-182631	101795	Stefano Morozzi	03/2022
8104	2^338155+187755	101795	Stefano Morozzi	04/2022
8105	2^338154-83975	101795	Stefano Morozzi	04/2022
8106	2^338154+163759	101795	Stefano Morozzi	05/2022
8107	2^338152-25767	101794	Stefano Morozzi	12/2021
8108	2^338152+181927	101794	Stefano Morozzi	02/2022
8109	2^338151+60779	101794	Stefano Morozzi	03/2022
8110	2^338151+189149	101794	Stefano Morozzi	05/2022
8111	2^338152+45567	101794	Stefano Morozzi	11/2022
8112	2^338147+29343	101793	Stefano Morozzi	01/2022
8113	2^338148+130803	101793	Stefano Morozzi	01/2022
8114	2^338146+166167	101793	Stefano Morozzi	06/2022
8115	2^338149-185073	101793	Stefano Morozzi	06/2022
8116	2^338149+41757	101793	Stefano Morozzi	09/2022
8117	2^338149+125015	101793	Stefano Morozzi	02/2023
8118	2^338144+180697	101792	Stefano Morozzi	01/2022
8119	2^338143+8589	101792	Stefano Morozzi	02/2022
8120	2^338143-55611	101792	Stefano Morozzi	02/2022
8121	2^338143+60623	101792	Stefano Morozzi	03/2022
8122	2^338145-63609	101792	Stefano Morozzi	12/2022
8123	2^338141-77301	101791	Stefano Morozzi	12/2021
8124	2^338141+157145	101791	Stefano Morozzi	02/2022
8125	2^338140+84745	101791	Stefano Morozzi	03/2022
8126	2^338140+90073	101791	Stefano Morozzi	05/2022
8127	2^338142+96583	101791	Stefano Morozzi	11/2022
8128	2^338139-134719	101790	Stefano Morozzi	04/2022
8129	2^338138+95443	101790	Stefano Morozzi	11/2022
8130	2^338133+1445	101789	Stefano Morozzi	12/2021
8131	2^338133+172469	101789	Stefano Morozzi	11/2022
8132	2^338134+23235	101789	Stefano Morozzi	11/2022
8133	2^338132+105643	101788	Stefano Morozzi	01/2022
8134	2^338131+181871	101788	Stefano Morozzi	02/2022
8135	2^338132-184539	101788	Stefano Morozzi	04/2022
8136	2^338130+22383	101788	Stefano Morozzi	11/2022
8137	2^338132+170143	101788	Stefano Morozzi	11/2022
8138	2^338131-62599	101788	Stefano Morozzi	12/2022
8139	2^338128+128953	101787	Stefano Morozzi	01/2022
8140	2^338127+11021	101787	Stefano Morozzi	03/2022
8141	2^338127+192935	101787	Stefano Morozzi	09/2022
8142	2^338127+98621	101787	Stefano Morozzi	11/2022
8143	2^338128+98853	101787	Stefano Morozzi	02/2023
8144	2^338123-25959	101786	Stefano Morozzi	12/2021
8145	2^338124-180765	101786	Stefano Morozzi	02/2022
8146	2^338125-7129	101786	Stefano Morozzi	03/2022
8147	2^338125-40071	101786	Stefano Morozzi	01/2023
8151	2^338122-20117	101785	Enzo Doria	06/2013
8152	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
8148	2^338122+32799	101785	Stefano Morozzi	02/2022
8149	2^338120+166411	101785	Stefano Morozzi	06/2022
8150	2^338122+90705	101785	Stefano Morozzi	06/2022
8153	2^338117+103761	101784	Stefano Morozzi	01/2022
8154	2^338118+53817	101784	Stefano Morozzi	01/2022
8155	2^338116+82585	101784	Stefano Morozzi	02/2022
8156	2^338118+39483	101784	Stefano Morozzi	05/2022
8157	2^338119+96659	101784	Stefano Morozzi	11/2022
8158	2^338115+61083	101783	Stefano Morozzi	03/2022
8159	2^338114+173287	101783	Stefano Morozzi	11/2022
8160	2^338113-139681	101783	Stefano Morozzi	01/2023
8161	2^338110-175365	101782	Stefano Morozzi	12/2021
8162	2^338110-3963	101782	Stefano Morozzi	01/2022
8163	2^338112+155061	101782	Stefano Morozzi	01/2022
8164	2^338112+137335	101782	Stefano Morozzi	04/2022
8165	2^338111-85627	101782	Stefano Morozzi	06/2022
8166	2^338111-90145	101782	Stefano Morozzi	01/2023
8175	35^65917-7092	101781	Enzo Doria	03/2013
8167	2^338107-1221	101781	Stefano Morozzi	12/2021
8168	2^338109+108539	101781	Stefano Morozzi	03/2022
8169	2^338109-7261	101781	Stefano Morozzi	03/2022
8170	2^338109-131961	101781	Stefano Morozzi	03/2022
8171	2^338108+39585	101781	Stefano Morozzi	05/2022
8172	2^338109+38147	101781	Stefano Morozzi	05/2022
8173	2^338108+17301	101781	Stefano Morozzi	09/2022
8174	2^338108-65859	101781	Stefano Morozzi	01/2023
8176	2^338105+79599	101780	Stefano Morozzi	01/2022
8177	2^338103-180675	101780	Stefano Morozzi	02/2022
8178	2^338103+19499	101780	Stefano Morozzi	09/2022
8179	2^338103-165319	101780	Stefano Morozzi	01/2023
8180	2^338100-100389	101779	Stefano Morozzi	12/2021
8181	2^338100+27595	101779	Stefano Morozzi	12/2021
8182	2^338101+101139	101779	Stefano Morozzi	12/2021
8183	2^338101+134985	101779	Stefano Morozzi	03/2022
8184	2^338102+186135	101779	Stefano Morozzi	03/2022
8185	2^338100+36885	101779	Stefano Morozzi	04/2022
8186	2^338102-8151	101779	Stefano Morozzi	04/2022
8187	2^338100+90637	101779	Stefano Morozzi	06/2022
8188	2^338101+68505	101779	Stefano Morozzi	09/2022
8189	2^338100-42867	101779	Stefano Morozzi	02/2023
8190	2^338097+100229	101778	Stefano Morozzi	11/2021
8191	2^338097-25695	101778	Stefano Morozzi	12/2021
8192	2^338098-110043	101778	Stefano Morozzi	06/2022
8193	2^338099-191389	101778	Stefano Morozzi	01/2023
8194	2^338093-128403	101777	Stefano Morozzi	01/2022
8195	2^338093+33051	101777	Stefano Morozzi	02/2022
8196	2^338094+135555	101777	Stefano Morozzi	03/2022
8197	2^338095-32395	101777	Stefano Morozzi	03/2022
8198	2^338090-175353	101776	Stefano Morozzi	12/2021
8199	2^338090+33277	101776	Stefano Morozzi	02/2022
8200	2^338091-105601	101776	Stefano Morozzi	02/2022
8201	2^338091-32127	101776	Stefano Morozzi	03/2022
8202	2^338092+12873	101776	Stefano Morozzi	04/2022
8203	2^338091-58485	101776	Stefano Morozzi	04/2022
8204	2^338086+177643	101775	Stefano Morozzi	12/2021
8205	2^338089+82905	101775	Stefano Morozzi	02/2022
8206	2^338088+87565	101775	Stefano Morozzi	04/2022
8207	2^338088-166205	101775	Stefano Morozzi	01/2023
8208	2^338089-140053	101775	Stefano Morozzi	01/2023
8209	2^338087+124935	101775	Stefano Morozzi	02/2023
8210	2^338085-3301	101774	Stefano Morozzi	01/2022
8211	2^338084+108691	101774	Stefano Morozzi	03/2022
8212	2^338083+164369	101774	Stefano Morozzi	05/2022
8213	2^338080+107521	101773	Stefano Morozzi	02/2022
8214	2^338080-156917	101773	Stefano Morozzi	03/2022
8215	2^338081+199775	101773	Stefano Morozzi	02/2023
8216	2^338076+62311	101772	Stefano Morozzi	04/2022
8217	2^338079+161745	101772	Stefano Morozzi	04/2022
8218	2^338078-60075	101772	Stefano Morozzi	06/2022
8219	2^338079+167079	101772	Stefano Morozzi	09/2022
8220	2^338076+122535	101772	Stefano Morozzi	11/2022
8221	2^338077+95619	101772	Stefano Morozzi	11/2022
8222	2^338078+20539	101772	Stefano Morozzi	11/2022
8223	2^338076-36813	101772	Stefano Morozzi	12/2022
8224	2^338078-64911	101772	Stefano Morozzi	01/2023
8225	2^338073-77971	101771	Stefano Morozzi	01/2022
8226	2^338074+55579	101771	Stefano Morozzi	01/2022
8227	2^338073-81813	101771	Stefano Morozzi	03/2022
8228	2^338073+138645	101771	Stefano Morozzi	05/2022
8229	2^338075+148043	101771	Stefano Morozzi	11/2022
8230	2^338070-152607	101770	Stefano Morozzi	01/2022
8231	2^338070+138787	101770	Stefano Morozzi	05/2022
8232	2^338071+165249	101770	Stefano Morozzi	06/2022
8233	2^338070+70359	101770	Stefano Morozzi	11/2022
8234	2^338071+98573	101770	Stefano Morozzi	11/2022
8235	2^338069+79365	101769	Stefano Morozzi	01/2022
8236	2^338069+107571	101769	Stefano Morozzi	02/2022
8237	2^338068+73035	101769	Stefano Morozzi	11/2022
8238	2^338064+100087	101768	Stefano Morozzi	11/2021
8239	2^338064-83793	101768	Stefano Morozzi	04/2022
8240	2^338064+193701	101768	Stefano Morozzi	09/2022
8241	2^338065+199947	101768	Stefano Morozzi	02/2023
8242	2^338060-151047	101767	Stefano Morozzi	12/2021
8243	2^338060-130805	101767	Stefano Morozzi	02/2022
8244	2^338060-136593	101767	Stefano Morozzi	12/2022
8245	2^338062-15725	101767	Stefano Morozzi	01/2023
8246	2^338058-76415	101766	Stefano Morozzi	12/2021
8247	2^338057+83865	101766	Stefano Morozzi	03/2022
8248	2^338057+86997	101766	Stefano Morozzi	04/2022
8249	2^338058+188589	101766	Stefano Morozzi	05/2022
8250	2^338058+68089	101766	Stefano Morozzi	09/2022

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